Internal problem ID [9634]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1306.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{3} y^{\prime \prime }+x^{2} y^{\prime }+\left (a \,x^{2}+b x +a \right ) y=0} \]
✓ Solution by Maple
Time used: 0.469 (sec). Leaf size: 69
dsolve(x^3*diff(diff(y(x),x),x)+x^2*diff(y(x),x)+(a*x^2+b*x+a)*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \operatorname {HeunD}\left (0, 8 a +4 b , 0, 8 a -4 b , \frac {x +1}{x -1}\right ) \left (c_{1} +c_{2} \left (\int \frac {1}{x \operatorname {HeunD}\left (0, 8 a +4 b , 0, 8 a -4 b , \frac {x +1}{x -1}\right )^{2}}d x \right )\right ) \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[(a + b*x + a*x^2)*y[x] + x^2*y'[x] + x^3*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
Not solved